TITLE:
Unique Measure for the Time-Periodic Navier-Stokes on the Sphere Navier-Stokes on the Sphere
AUTHORS:
Gregory Varner
KEYWORDS:
Navier-Stokes, Invariant Measure, Sphere
JOURNAL NAME:
Applied Mathematics,
Vol.6 No.11,
October
16,
2015
ABSTRACT: This paper proves the existence and uniqueness of a time-invariant measure for the 2D Navier-Stokes equations on the sphere under a random kick-force and a time-periodic deterministic force. Several examples of deterministic force satisfying the necessary conditions for a unique invariant measure to exist are given. The support of the measure is examined and given explicitly for several cases.